The present paper concerns the study of the nonconservative bitem-perature Euler system with transverse magnetic field. We firstly introduce an underlying conservative kinetic model coupled to Maxwell equations. The nonconservative bitemperature Euler system with transverse magnetic field is then established from this kinetic model by hydrodynamic limit. Next we present the derivation of a finite volume method to approximate weak solutions. It is obtained by solving a relaxation system of Suliciu type, and is similar to HLLC type solvers. The solver is shown in particular to preserve positivity of density and internal energies. Moreover we use a local minimum entropy principle to prove discrete entropy inequalities, ensuring the robustness of the scheme.

中文翻译：

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具有横向磁场的非保守双温欧拉系统的建模和熵满足弛豫方案

本论文涉及具有横向磁场的非保守双温欧拉系统的研究。我们首先介绍了一个与麦克斯韦方程耦合的潜在保守动力学模型。然后由该动力学模型通过流体动力学极限建立具有横向磁场的非守恒双温欧拉系统。接下来，我们将介绍一种有限体积方法的推导来逼近弱解。它是通过求解 Suliciu 型松弛系统获得的，类似于 HLLC 型求解器。求解器特别显示为保持密度和内能的正性。此外，我们使用局部最小熵原理来证明离散熵不等式，确保方案的鲁棒性。